1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pogonyaev
3 years ago
11

The costs of 5 similar digital cameras and 3 similar video cameras is $3,213. Each video camera costs 4 times as much as each di

gital camera. John buys a digital camera and a video camera. How much does he pay?
Mathematics
1 answer:
mariarad [96]3 years ago
7 0
Let,
digital cameras be "x"
video cameras be "y"
Now,
According to the question,
5x + 3y = $3,213..................................................equation (1)
y = 4x..................................................................equation (2)

Taking equation (1)
5x + 3y = $3,213
Substituting the value of "y" from equation (2), we get,
5x + 3(4x) = $3,213
5x + 12x = $3,213
17x = $3,213
x = $3,213 / 17
x = $189

Taking equation (2)
y = 4x
Substituting the value of "x", we get,
y = 4 ($189)
y = $756

Now,
John buys a digital and a video camera. So, it costs him ($189 + $756) = $945

You might be interested in
7/2 in a<br> Mixed fraction
nasty-shy [4]
2 goes into 7, 3 times and you keep 2 the denominator and there is 1 left over so its
3 1/2
5 0
3 years ago
1)<br> I<br> I<br> ? 20-<br> A) 999<br> C) 1219<br> B) 39°<br> D) 1020
WITCHER [35]

Answer:

C

Step-by-step explanation:

\angle{VUW} = 180 - 141 = 39

\angle{WVU} = 180 - (20 + 39) = 121

Answer: 121

8 0
3 years ago
The circumference of a circle is 65?. In terms of pi, what is the area of the circle?
iVinArrow [24]

Answer:

1056.25π square units

Step-by-step explanation:

A few formulas an definitions which will help us:

(1) \pi=\frac{c}{d}, where c is the circumference of a circle and d is its diameter

(2) A=\pi r^2, where A is the area of a circle with radius r. To put it in terms of d, remember that a circle's diameter is simply twice its radius, or mathematically, (3) d=2r \rightarrow r=\frac{d}{2}.

We can rearrange equation (1) to put d in terms of π and c, giving us (4) d = \frac{c}{\pi}, and we can make a few substitutions in (2) using (3) and (4) to get use the area in terms of the circumference and π:

A=\pi r^2\\=\pi\left(\frac{d}{2}\right)^2\\=\pi\left(\frac{d^2}{4}\right)\\=\pi\left(\frac{(c/\pi)^2}{4}\right)\\=\pi\left(\frac{c^2/\pi^2}{4}\right)\\=\pi\left(\frac{c^2}{4\pi^2}\right)\\\\=\frac{\pi c^2}{4\pi^2}\\ =\frac{c^2}{4\pi}

We can now substitute c for our circumference, 65, to get our answer in terms of π:

A=\dfrac{65^2}{4\pi}=\dfrac{4225}{4\pi}=1056.25\pi

8 0
3 years ago
Read 2 more answers
GEOMETRY. PLEASE HELP ASAP!! I AM STUMPED! O.o
vagabundo [1.1K]

The point R has coordinates (-5,-5) and the image point R' has coordinates (2,-7).

If

  • -5+a=2, then a=2-(-5)=2+5=7;
  • -5+b=-7, then b=-7-(-5)=-7+5=-2.

Thus, the translation rule is

(x,y)→(x+7,y-2)

or T_{(7,-2)}(RSTU)

If point U has coordinates (-5,1), then its image U' has coordinates (-5+7,1-2) that is (2,-1).

Answer: correct choice is B

4 0
3 years ago
Find a formula for the least squares solution of ax=b when the columns of a are orthonormal1 .
neonofarm [45]
Let \mathbf A be a rectangular m\times n matrix with column vectors \mathbf a_1,\ldots,\mathbf a_n, i.e.

\mathbf A=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}

Then we have

\mathbf A^\top=\begin{bmatrix}\mathbf a_1&\cdots&\mathbf a_n\end{bmatrix}^\top

and the product of the two is

\mathbf A^\top\mathbf A=\begin{bmatrix}\mathbf a_1\cdot\mathbf a_1&\mathbf a_1\cdot\mathbf a_2&\cdots&\mathbf a_1\cdot\mathbf a_n\\\mathbf a_2\cdot\mathbf a_1&\mathbf a_2\cdot\mathbf a_2&\cdots&\mathbf a_2\cdot\mathbf a_n\\\vdots&\vdots&\ddots&\vdots\\\mathbf a_n\cdot\mathbf a_1&\mathbf a_n\cdot\mathbf a_2&\cdots&\mathbf a_n\cdot\mathbf a_n\end{bmatrix}

Because the columns of \mathbf A are orthonormal, we have

\mathbf a_i\cdot\mathbf a_j=\begin{cases}1&\text{for }i=j\\0&\text{for }i\neq j\end{cases}

which means \mathbf A^\top\mathbf A reduces to an n\times n matrix with ones along the diagonal and zero everywhere else, i.e.

\mathbf A^\top\mathbf A=\begin{bmatrix}1&0&\cdots&0\\0&1&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&0&\cdots&1\end{bmatrix}=\mathbf I_n

where \mathbf I denotes the identity matrix. This means the solution to \mathbf{Ax}=\mathbf b is given by

\mathbf A^\top(\mathbf{Ax})=\mathbf A^\top\mathbf b\implies(\underbrace{\mathbf A^\top\mathbf A}_{\mathbf I})\mathbf x=\mathbf A^\top\mathbf b\implies\mathbf x=\mathbf A^\top\mathbf b
6 0
3 years ago
Other questions:
  • What times what equals to 130
    7·1 answer
  • El histograma muestra los pesos en libras de equipaje facturado en un vuelo
    15·1 answer
  • The following frequency table shows the number of Jui's pictures that have been published in each of the local
    15·1 answer
  • Answer this pls! Fast
    5·1 answer
  • Identify the domain of the function.
    10·1 answer
  • PLS HELP ASAP WILL GIVE BRAINlEST AND 100 POINTS
    11·1 answer
  • I need help with this​
    14·1 answer
  • (4y^4)^2 without exponents
    10·2 answers
  • Nina is selling three types of energy bars at a market stall. She bought 60 Enerbars at 40p per bar and 200 Grainbars at 60p per
    5·1 answer
  • Please help!!!!!!!!!
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!